Abstract: The EEPAS medium-term earthquake clustering model, which is based on the precursory scale increase and associated predictive scaling relations, uses the bivariate normal distribution for location of future earthquake occurrences in relation to the location of a contributing earthquake. This means that the estimated future earthquake activity tends to highest at the locations of past earthquakes in the catalogue. Estimates of future earthquake occurrence rates in Canterbury, using a hybrid model including the EEPAS model along with several others, show this feature. On the other hand, ideas about stress transfer suggest that the earthquake activity should migrate away from Christchurch city in the medium term. We develop alternatives to the bivariate normal distribution, in which the spatial distribution has the shape either of a donut (with a depressed rate close to the epicentre of the contributing earthquake), or of a witch’s hat (with an elevated rate close to the epicentre), and fit these alternative distributions in variations of the EEPAS model applied to New Zealand earthquakes over the period 1987-2006. The results show that there is no information gain from using either the donut distribution or a mixture of the donut and bivariate normal distributions, and if anything, the witch’s hat distribution is preferred over either of these models. Further, even if the donut distribution were to be adopted, it would have little effect in moving the estimates of future earthquake activity away from Christchurch city. (auth)